Properties

Conductor 4020
Order 132
Real No
Primitive Yes
Parity Odd
Orbit Label 4020.dq

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(4020)
 
sage: chi = H[47]
 
pari: [g,chi] = znchar(Mod(47,4020))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4020
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 132
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Odd
Orbit label = 4020.dq
Orbit index = 95

Galois orbit

sage: chi.sage_character().galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{4020}(23,\cdot)\) \(\chi_{4020}(47,\cdot)\) \(\chi_{4020}(83,\cdot)\) \(\chi_{4020}(167,\cdot)\) \(\chi_{4020}(227,\cdot)\) \(\chi_{4020}(287,\cdot)\) \(\chi_{4020}(323,\cdot)\) \(\chi_{4020}(467,\cdot)\) \(\chi_{4020}(743,\cdot)\) \(\chi_{4020}(827,\cdot)\) \(\chi_{4020}(887,\cdot)\) \(\chi_{4020}(1127,\cdot)\) \(\chi_{4020}(1223,\cdot)\) \(\chi_{4020}(1283,\cdot)\) \(\chi_{4020}(1463,\cdot)\) \(\chi_{4020}(1523,\cdot)\) \(\chi_{4020}(1547,\cdot)\) \(\chi_{4020}(1643,\cdot)\) \(\chi_{4020}(1763,\cdot)\) \(\chi_{4020}(2003,\cdot)\) \(\chi_{4020}(2027,\cdot)\) \(\chi_{4020}(2087,\cdot)\) \(\chi_{4020}(2183,\cdot)\) \(\chi_{4020}(2267,\cdot)\) \(\chi_{4020}(2327,\cdot)\) \(\chi_{4020}(2447,\cdot)\) \(\chi_{4020}(2483,\cdot)\) \(\chi_{4020}(2567,\cdot)\) \(\chi_{4020}(2783,\cdot)\) \(\chi_{4020}(2807,\cdot)\) ...

Values on generators

\((2011,2681,3217,1141)\) → \((-1,-1,i,e\left(\frac{25}{33}\right))\)

Values

-117111317192329313741
\(-1\)\(1\)\(e\left(\frac{23}{132}\right)\)\(e\left(\frac{23}{33}\right)\)\(e\left(\frac{19}{132}\right)\)\(e\left(\frac{31}{132}\right)\)\(e\left(\frac{19}{33}\right)\)\(e\left(\frac{127}{132}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{7}{66}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{43}{66}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{132})\)